arXiv subjects

Nan Liang

Publications and source records attributed to Nan Liang.

At least 19 recordsLinked to original sources

arXiv2025

Testing the Distance Duality Relation with Cosmological Observations at high Redshift using Artificial Neural Network

The cosmic Distance Duality Relation (DDR) is a fundamental prediction of metric gravity under photon number conservation. In this work, we perform a model-independent test of the DDR using Pantheon+ type Ia supernovae (SN Ia), \emph{Fermi} gamma-ray bursts (GRBs) with the FULL and GOLD samples, the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) baryon acoustic oscillation (BAO) measurements, and the galaxy-scale strong gravitational lensing (SGL) system samples at high redshift $0.01 < z \lesssim 8$ using an artificial neural network (ANN) approach. Our results show that the standard DDR is consistent with cosmological observations at high redshift within the $\sim 2 \sigma$ confidence level.

astro-ph.CO↗

arXiv2025

Cosmological Constraints on the Phenomenological Interacting Dark Energy Model with Fermi Gamma-Ray Bursts and DESI DR2

In this work, we constrain the phenomenological interacting dark energy (IDE) model using \emph{Fermi} gamma-ray burst (GRB) dataset and the latest baryon acoustic oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2). Through a joint Bayesian analysis, we perform a cosmological comparative assessment of the $\Lambda$CDM, $w$CDM, and CPL models with the phenomenological IDE model. For the phenomenological IDE model in a flat universe with \emph{Fermi} samples and DESI DR2, we obtain: $\xi=2.63^{+0.63}_{-0.52}$, $\xi + 3w_X = -0.98^{+1.90}_{-2.07}$ with the GOLD sample ($1.4\le z \le5.6$) and $\xi=2.83^{+0.63}_{-0.58}$, $\xi + 3w_X = 0.03^{+1.35}_{-1.33}$ with the FULL sample ($1.4\le z \le8.2$), respectively. Our analysis shows that the $\Lambda$CDM model without interaction ($\xi=3$, $\xi + 3w_X = 0$) is consistent with the latest \emph{Fermi} sample and DESI DR2 at $1\sigma$ confidence level. We find no significant deviations from the standard model using AIC and BIC criterias.

astro-ph.CO↗

arXiv2025

Testing the Cosmic Distance Duality Relation with Neural Kernel Gaussian Process Regression

In this work, we test the cosmic distance duality relation (CDDR) by combining Pantheon+ Type Ia supernova (SNe Ia) data and DESI DR2 baryon acoustic oscillation (BAO) measurements. To resolve the redshift mismatch between the two datasets, we develop a new method called Neural Kernel Gaussian Process Regression (NKGPR), which uses two neural networks to simultaneously learn the mean and kernel functions of a Gaussian process. This approach improves upon traditional Gaussian process regression by mitigating trend mismatches and removing the need for manual kernel selection. We investigate possible deviations from the CDDR by adopting three parameterizations of the deviation function and constrain the model-independent parameter $\eta_0$ through a marginalized likelihood analysis. Our results show no significant departure from the expected relation, confirming the consistency of the CDDR within current observational uncertainties.

astro-ph.CO↗

arXiv2025

Gamma-Ray Bursts Calibrated by Using Artificial Neural Networks from the Pantheon+ Sample

In this paper, we calibrate the luminosity relation of gamma-ray bursts (GRBs) by Artificial Neural Networks (ANN) which is employed to analyze the Pantheon+ sample of type Ia supernovae (SNe Ia) in a manner independent of cosmological assumptions. The A219 GRB dataset are used to calibrate the Amati relation ($E_{\rm p}$-$E_{\rm iso}$) at low redshift with the ANN framework, facilitating the construction of the Hubble diagram at higher redshifts. Cosmological models are constrained with GRBs at high-redshift and the latest observational Hubble data (OHD) via a Markov Chain Monte Carlo numerical approach. For the Chevallier-Polarski-Linder (CPL) model within a flat universe, we obtain $\Omega_{\rm m} = 0.321^{+0.078}_{-0.069}$, $h = 0.654^{+0.053}_{-0.071}$, $w_0 = -1.02^{+0.67}_{-0.50}$, and $w_a = -0.98^{+0.58}_{-0.58}$ at the 1-$\sigma$ confidence level, which indicating a preference for dark energy with potential redshift evolution ($w_a \neq 0$). These findings by using ANN align closely with those derived from GRBs calibrated by using Gaussian Processes.

astro-ph.CO↗

arXiv2025

Gamma-Ray Bursts Calibrated from the Observational $H(z)$ Data in Artificial Neural Network Framework

In this paper, we calibrate the luminosity relation of gamma-ray bursts (GRBs) from an Artificial Neural Network (ANN) framework for reconstructing the Hubble parameter \unboldmath{$H(z)$} from the latest observational Hubble data (OHD) obtained with the cosmic chronometers method in a cosmology-independent way. We consider the physical relationships between the data to introduce the covariance matrix and KL divergence of the data into the loss function and calibrate the Amati relation ($E_{\rm p}$--$E_{\rm iso}$) by selecting the optimal ANN model with the A219 sample and the J220 sample at low redshift. Combining the Pantheon+ type Ia supernovae (SNe Ia) sample and Baryon acoustic oscillations (BAOs) from Dark Energy Spectroscopy Instrument (DESI) with GRBs at high redshift in the Hubble diagram by Markov Chain Monte Carlo numerical method, we find that the $\Lambda$CDM model is preferred over the $w$CDM and CPL models with joint constraints by the Akaike Information Criterion and Bayesian Information Criterion.

astro-ph.CO↗

arXiv2024

Testing the phenomenological interacting dark energy model with gamma-ray bursts and Pantheon+ type Ia supernovae

In this paper, we utilize recent observational data from gamma-ray bursts (GRBs) and Pantheon+ supernovae Ia (SNe Ia) sample to explore the interacting dark energy (IDE) model in a phenomenological scenario. Results from GRBs alone, SNe Ia and GRBs+SNe Ia indicate that the energy is transferred from dark energy to dark matter and the coincidence problem is alleviated. The value of $H_0$ from GRBs+SNe Ia in the IDE scenario shows agreement with the SH0ES measurement. Considering the age estimate of the quasar APM 08279+5255 at $z = 3.91$, we find that the phenomenological IDE scenario can predict a cosmic age greater than that of the $\Lambda$CDM model, thus the cosmic age problem can be alleviated.

astro-ph.CO↗

arXiv2024

Constraints from Fermi observations of Long Gamma-Ray Bursts on cosmological parameters

In this paper, we compile a \emph{Fermi} sample of the \emph{long} GRB observations from 15 years of GBM catalogue with identified redshift, in which the GOLD sample contains 123 long GRBs at $z\le5.6$ and the FULL sample contains 151 long GRBs with redshifts at $z\le8.2$. The Amati relation (the $E_{\rm p,i}$-$E_{\rm iso}$ correlation) are calibrated at $z<1.4$ by a Gaussian Process from the latest observational Hubble data (OHD) with the cosmic chronometers method so that GRBs at high-redshift $z\ge1.4$ can be used to constrain cosmological models via the Markov chain Monte Carlo (MCMC) method. From the cosmology-independent GRBs with the GOLD sample at $z\ge1.4$ and the Pantheon+ sample of type Ia supernovae (SNe Ia) at $0.01<z\leq2.3$, we obtain $\Omega_{\rm m} = 0.354\pm0.018, H_0 = 73.05\pm0.2\,\rm{km/s/Mpc}$ for the flat $\Lambda$CDM model; $w_0 = -1.22^{+0.18}_{-0.15}$ for the flat $w$CDM model; and $w_{a} = -1.12^{+0.45}_{-0.83}$ for the flat Chevallier-Polarski-Linder model at the 1$\sigma$ confidence level. Our results with the GOLD and FULL sample are almost identical, which are more stringent than the previous results with GRBs.

astro-ph.CO↗

arXiv2024

Constraints on Cosmological Models from Quasars Calibrated with Type Ia Supernova by a Gaussian Process

In this paper, we use quasars calibrated from type Ia supernova (SN Ia) to constrain cosmological models. We consider three different X-ray luminosity ($L_{X}$) - ultraviolet luminosity ($L_{UV}$) relations of quasars, i.e., the standard $L_{X}$-$L_{UV}$ relation and two redshift-evolutionary relations (Type I and Type II) respectively constructed from copula and considering a redshift correction to the luminosity of quasars. Only in the case of the Type I relation, quasars can always provide effective constraints on the $\Lambda$CDM model. Furthermore, we show that, when the observational Hubble data (OHD) are added, the constraints on the absolute magnitude $M$ of SN Ia and the Hubble constant $H_0$ can be obtained. In the $\Lambda$CDM model, the OHD measurements plus quasars with the Type I relation yields $M$ =$-19.321^{+0.085}_{-0.076}$, which is in good agreement with the measurement from SH0ES ($M=-19.253\pm{0.027}$), and $H_0$ = $70.80\pm3.6~\mathrm{km~s^{-1}Mpc^{-1}}$, falling between the measurements from SH0ES and the Planck cosmic microwave background radiation data.

astro-ph.CO↗

arXiv2024

Constraining the emergent dark energy models with observational data at intermediate redshift

In this work, we investigate the phenomenologically emergent dark energy (PEDE) model and its generalized form, namely the generalized emergent dark energy (GEDE) model, which introduces a free parameter \unboldmath {$ \Delta $} that can discriminate between the \unboldmath{$\mathrm{\Lambda}$}CDM model and the PEDE model. Fitting the emergent dark energy (EDE) models with the observational datasets including the cosmology-independent gamma-ray bursts (GRBs) and the observational Hubble data (OHD) at intermediate redshift, we find a large value of $H_0$ which is close to the results of local measurement of $H_0$ from the SH0ES Collaboration in both EDE models. In order to refine our analysis and tighten the constraints on cosmological parameters, we combine mid-redshift observations GRBs and OHD with baryon acoustic oscillations (BAOs). Finally, we constrain DE models by using the simultaneous fitting method, in which the parameters of DE models and the relation parameters of GRBs are fitted simultaneously. Our results suggest that PEDE and GEDE models can serve as an important supplement and be possible alternative to the standard cosmological model, pending further theoretical explorations and observational verifications.

astro-ph.CO↗

arXiv2023

Model-independent Gamma-Ray Bursts Constraints on Cosmological Models Using Machine Learning

In this paper, we calibrate the luminosity relation of gamma-ray bursts (GRBs) with the machine learning (ML) algorithms from the Pantheon+ sample of type Ia supernovae in a cosmology-independent way. By using K-Nearest Neighbors (KNN) and Random Forest (RF) selected with the best performance in the ML algorithms, we calibrate the Amati relation (\unboldmath{$E_{\rm p}$-$E_{\rm iso}$}) relation with the A219 sample to construct the Hubble diagram of GRBs. Via the Markov Chain Monte Carlo numerical method with GRBs at high redshift and latest observational Hubble data, we find the results of constraints on cosmological models by using KNN and RF algorithms are consistent with those obtained from GRBs calibrated by using the Gaussian Process.

astro-ph.CO↗

arXiv2023

Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way

In this paper, we present a cosmology-independent method to constrain cosmological models from the latest 221 gamma-ray bursts (GRBs) sample, including 49 GRBs from Fermi catalog with the Amati relation (the $E_{\rm p}$-${E}_{\rm iso}$ correlation), which are calibrated by using a Gaussian process from the Pantheon+ type Ia supernovae (SNe Ia) sample. With 182 GRBs at $0.8\le z\le8.2$ in the Hubble diagram and the latest observational Hubble data (OHD) by the Markov Chain Monte Carlo (MCMC) method, we obtained $\Omega_{\rm m}$ = $0.348^{+0.048}_{-0.066}$ and $h$ = $0.680^{+0.029}_{-0.029}$ for the flat $\Lambda$CDM model, and $\Omega_{\rm m}$ = $0.318^{+0.067}_{-0.059}$, $h$ = $0.704^{+0.055}_{-0.068}$, $w$ = $-1.21^{+0.32}_{-0.67}$ for the flat $w$CDM model. These results are consistent with those in which the coefficients of the Amati relation and the cosmological parameters fitted simultaneously.

astro-ph.CO↗

arXiv2023

Testing Dark Energy Models with Gamma-Ray Bursts Calibrated from the Observational $H(z)$ Data through a Gaussian Process

We use a cosmology-independent method to calibrate gamma-ray burst (GRB) from the observational Hubble data (OHD) with the cosmic chronometers method. By using Gaussian Process to reconstruct OHD, we calibrate the Amati relation ($E_{\rm p}$--$E_{\rm iso}$) to construct a GRB Hubble diagram with the A118 data set, and constrain Dark Energy models in a flat space with the Markov Chain Monte Carlo numerical method. With the cosmology-independent GRBs at $1.4<z\leq8.2$ in the A118 data set and the Pantheon sample of type Ia supernovae (SNe Ia) at $0.01<z\leq2.3$, we obtained $Ω_{\rm m}$ = $0.379^{+0.033}_{-0.024}$, $h$ = $0.701^{+0.0035}_{-0.0035}$, $w$ = $-1.25^{+0.14}_{-0.12}$, $w_a$ = $-0.84^{+0.81}_{-0.38}$ for the flat Chevallier-Polarski-Linder model at the 1$σ$ confidence level. We find no significant evidence supporting deviations from the standard $Λ$CDM model.

astro-ph.CO↗

arXiv2022

Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae

In this paper, we calibrate the Amati relation (the $E_{\rm p}$-${E}_{\rm iso}$ correlation) of gamma-ray bursts (GRBs) in a cosmology-independent way. By using Gaussian process to reconstruct the smoothed luminosity distance from the Pantheon type Ia supernovae (SNe Ia) sample, we utilize the reconstructed results to calibrate the $E_{\rm p}$-${E}_{\rm iso}$ correlation with the Markov Chain Monte Carlo method and construct a Hubble diagram with the A220 GRB data, in which there are A118 GRB data with the higher qualities appropriate for cosmological purposes. With 98 GRBs at $1.4<z\leq8.2$ in the A118 sample and the observed Hubble data, we obtain $Ω_{\rm m}$=$0.346^{+0.048}_{-0.069}$, $h$=$0.677^{+0.029}_{-0.029}$ for the flat $Λ$CDM model, and $Ω_{\rm m}$=$0.314^{+0.072}_{-0.055}$, $h$=$0.705^{+0.055}_{-0.069}$, $w$=$-1.23^{+0.33}_{-0.64}$ for the flat $w$CDM model, which are consistent with those from fitting the coefficients of the Amati relation and the cosmological parameters simultaneously.

astro-ph.CO↗

arXiv2022

Redshift-evolutionary X-ray and UV luminosity relation of quasars from Gaussian copula

We construct a three-dimensional and redshift-evolutionary X-ray and ultraviolet ($L_X-L_{UV}$) luminosity relation for quasars from the powerful statistic tool called copula, and find that the constructed $L_X-L_{UV}$ relation from copula is more viable than the standard one and the observations favor the redshift-evolutionary relation more than $3σ$. The Akaike and Bayes information criterions indicate that the quasar data support strongly the three-dimensional $L_X-L_{UV}$ relation. Our results show that the quasars can be regarded as a reliable indicator of the cosmic distance if the $L_X-L_{UV}$ relation from copula is used to calibrate quasar data.

astro-ph.CO↗

arXiv2022

Gamma ray burst constraints on cosmological models from the improved Amati correlation

An improved Amati correlation was constructed in (ApJ 931 (2022) 50) by us recently. In this paper, we further study constraints on the $Λ$CDM and $w$CDM models from the gamma ray bursts (GRBs) standardized with the standard and improved Amati correlations, respectively. By using the Pantheon type Ia supernova sample to calibrate the latest A220 GRB data set, the GRB Hubble diagram is obtained model-independently. We find that at the high redshift region ($z>1.4$) the GRB distance modulus from the improved Amati correlation is larger apparently than that from the standard Amati one. The GRB data from the standard Amati correlation only give a lower bound limit on the present matter density parameter $Ω_{\mathrm{m0}}$, while the GRBs from the improved Amati correlation constrain the $Ω_{\mathrm{m0}}$ with the $68\%$ confidence level to be $0.308^{+0.066}_{-0.230}$ and $0.307^{+0.057}_{-0.290}$ in the $Λ$CDM and $w$CDM models, respectively, which are consistent very well with those given by other current popular observational data including BAO, CMB and so on. Once the $H(z)$ data are added in our analysis, the constraint on the Hubble constant $H_0$ can be achieved. We find that two different correlations provide slightly different $H_0$ results but the marginalized mean values seem to be close to that from the Planck 2018 CMB observations.

astro-ph.CO↗

arXiv2022

The improved Amati correlations from Gaussian copula

In this paper, we obtain two improved Amati correlations of the Gamma-Ray burst (GRB) data via a powerful statistical tool called copula. After calibrating, with the low-redshift GRB data, the improved Amati correlations based on a fiducial $Λ$CDM model with $Ω_\mathrm{m0}=0.3$ and $H_0=70~\mathrm{km~s^{-1}Mpc^{-1}}$, and extrapolating the results to the high-redshift GRB data, we obtain the Hubble diagram of GRB data points. Applying these GRB data to constrain the $Λ$CDM model, we find that the improved Amati correlation from copula can give a result well consistent with $Ω_\mathrm{m0}=0.3$, while the standard Amati and extended Amati correlations do not. This results suggest that when the improved Amati correlation from copula is used in the low-redshift calibration method, the GRB data can be regarded as a viable cosmological explorer. However, the Bayesian information criterion indicates that the standard Amati correlation remains to be favored mildly since it has the least model parameters. Furthermore, once the simultaneous fitting method rather than the low-redshift calibration one is used, there is no apparent evidence that the improved Amati correlation is better than the standard one. Thus, more works need to be done in the future in order to compare different Amati correlations.

astro-ph.CO↗

arXiv2021

Pricing S&P 500 Index Options with Lévy Jumps

We analyze various jumps for Heston model, non-IID model and three Lévy jump models for S&P 500 index options. The Lévy jump for the S&P 500 index options is inevitable from empirical studies. We estimate parameters from in-sample pricing through SSE for the BS, SV, SVJ, non-IID and Lévy (GH, NIG, CGMY) models by the method of Bakshi et al. (1997), and utilize them for out-of-sample pricing and compare these models. The sensitivities of the call option pricing for the Lévy models with respect to parameters are presented. Empirically, we show that the NIG model, SV and SVJ models with estimated volatilities outperform other models for both in-sample and out-of-sample periods. Using the in-sample optimized parameters, we find that the NIG model has the least SSE and outperforms the rest models on one-day prediction.

q-fin.MF↗

arXiv2013

Interaction between dark energy and dark matter: observational constraints from OHD, BAO, CMB and SNe Ia

In order to test if there is energy transfer between dark energy and dark matter, we investigate cosmological constraints on two forms of nontrivial interaction between the dark matter sector and the sector responsible for the acceleration of the universe, in light of the newly revised observations including OHD, CMB, BAO and SNe Ia. More precisely, we find the same tendencies for both phenomenological forms of the interaction term $Q=3γHρ$, i.e., the parameter $γ$ to be a small number, $|γ|\approx 10^{-2}$. However, concerning the sign of the interaction parameter, we observe that $γ>0$ when the interaction between dark sectors is proportional to the energy density of dust matter, whereas the negative coupling ($γ<0$) is preferred by observations when the interaction term is proportional to dark energy density. We further discuss two possible explanations to this incompatibility and apply a quantitative criteria to judge the severity of the coincidence problem. Results suggest that the $γ_m$IDE model with a positive coupling may alleviate the coincidence problem, since its coincidence index $C$ is smaller than that for the $γ_d$IDE model, the interacting quintessence and phantom models by four orders of magnitude.

astro-ph.CO↗